Ch. 21 Magnetic Forces and Magnetic Fields
Relationship between electricity and magnetism
· Electricity and magnetism are intricately related. Magnetic fields can exert a force on moving charges and moving charges produce magnetic fields. In fact, the ultimate source of all magnetic fields is electric current, whether from the current in a wire or current produced by the motion of charges within atoms or molecules.
Properties of permanent magnets
1. Like poles repel, unlike attract (below left).
2. As shown below center, objects are most strongly attracted to the ends of bar magnets (N and S pole); highest concentration of magnetic field lines.
3. Magnetic poles always occur in pairs (dipoles). As shown below right, no matter how many times a bar magnet is cut in half, there is always a north and a south pole, even in the smallest piece. In fact, if we break the magnet down into subatomic parts, we find that even the electrons, protons, and neutrons within atoms behave as magnetic dipoles (that is, very little bar magnets). As it turns out, the magnetic effect of a bar magnet arises from the combination of the effects of the little bar magnets in the electrons in iron, nickel, or cobalt. Each electron’s magnet is small, but when you turn them in the same direction and add them all up, the total effect is strong.
Uniformly aligned magnetic domains produce magnetic fields in ferromagnetic materials
· Magnetism can be induced in ferromagnetic materials. Ferromagnetic materials are substances such as iron, cobalt, and nickel that exhibit magnetic properties when exposed to an external magnetic field. Magnetism in a substance is a result of the alignment of the magnetic domains. Magnetic domains are groups of atoms that have the same magnetic dipole orientation. In unmagnetized ferromagnetic substances, the domains are randomly arranged. In ferromagnetic substances exhibiting magnetic properties, the domains are predominantly aligned in one direction. If the domains can be permanently and uniformly aligned, a permanent magnet is produced.
Magnetic fields
· A permanent magnet or a moving charge will produce a magnetic field. To describe any type of field (electric, gravitational, or magnetic), we must define both the magnitude and the direction of the field. For magnetic fields, the following two conventions are used:
1. Direction of the magnetic field, B, at any location is the direction in which the N pole of a compass needle points at that location. For a permanent magnet, arrows originate on the N pole and terminate on S pole. The diagrams below show the magnetic field lines around a permanent magnet (a) and various current carrying conductors (b through e).
2. Magnitude of magnetic field is determined by the force the field exerts on a moving charge B=F/(qv sinq).
Magnetic field of the Earth
· The Earth’s magnetic field is due to the movement of charges in convection currents beneath the earth’s crust. As you can see in picture below, the north pole of a compass needle will point towards a point on the globe just north of Hudson Bay. Since unlike poles attract, this must mean that the earth’s south magnetic pole is near the earth’s geographic North Pole. Also, since the magnetic pole does not line up with the geographic pole, the difference between the two must be taken into account when using a compass for navigation. Magnetic declination is the difference between true north and the magnetic South Pole.
Magnetic field of a long, straight current carrying wire
· Moving charges produce magnetic fields. The direction of the field is always perpendicular to the direction of the moving charge (circular around the motion of the charge). The direction of the magnetic field produced by a moving charge can be found by using the right hand thumb rule. Point your thumb in the direction of the current (flow of positive charge) and your fingers coil in the direction of the field.
· By varying current and distance from the wire, one finds that B is proportional to the current and inversely proportional to the distance from the wire (B=moI/(2pr)).
Example 1: The two long straight wires shown below are perpendicular, insulated from each other, and small enough so that they may be considered to be in the same plane. The wires are not free to move. Point P, in the same plane as the wires, is 0.5 meter from the wire carrying a current of 1 ampere and is 1.0 meter from the wire carrying a current of 3 amperes.
a. What is the direction of the net magnetic field at P due to the currents?
b. Determine the magnitude of the net magnetic field at P due to the currents.
Magnetic field of a current loop
· Magnetic field set up by a current loop is similar to that of a bar magnet. The polarity of the loop of wire can be found using your right hand. Coil your fingers in the direction of the current and your thumb will point north.
Magnetic field of a solenoid
· A solenoid or electromagnet is a device consisting of a wire bent into a coil of several closely spaced loops that is magnetic when a current passes through the coil. The magnetic field inside the solenoid is nearly uniform and strong, but the magnetic field outside is relatively weak. Solenoids have many useful applications since they are magnetic only when they carry a current. The polarity of a solenoid can be found the same way you found the polarity of a current carrying loop. Coil your fingers in the direction of the current and your thumb will point north. The strength of the magnetic field depends upon the magnitude of the current, the number of coils per unit length, and whether or not an iron (ferromagnetic) core is inserted.
Motion of a charged particle in a magnetic field
· Since a moving charge creates a magnetic field around itself, it will feel a force when it moves through an external magnetic field. In order for a charge to experience a magnetic force, the following two conditions must be met:
1. The charge must be moving, for no magnetic force acts on a stationary charge.
2. The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field; parallel motion experiences no force.
· The magnitude of the force depends upon the strength of the field, the magnitude of the charge, and the component of the velocity that is perpendicular to the field
FB=qvB sinq
· Direction of the force can be found using right hand rule (if the charge is negative, know that the force is oppositely directed or just to use your left hand). To use the right hand rule, point fingers in direction of the magnetic field, thumb in direction of the velocity of a positive charge, and the palm of your hand will point in the direction of the force
· Application of the right hand rule at any point shows that the magnetic force is always toward the center of a circular path. The magnetic force is effectively a centripetal force that changes only the direction of the velocity and not the magnitude. If the charged particle is moving perpendicular to the magnetic field, it will follow a circular path. The path will be spiral if only a component of the velocity is perpendicular to the field. Since the magnetic force is a centripetal force, the magnetic force can do no work on a charged particle. That is, the magnetic force cannot change the speed or the kinetic energy of a particle.
· A mass spectrometer is a device that uses the magnetic force on a charged particle to determine the relative mass and abundance of an isotope or to help identify unknown particles. Particles are first ionized, and then accelerated through a known potential difference into a uniform magnetic field where the trajectory changes and hits a detector. By knowing the relative field strengths, charge, and the radius of the path, the particles mass can be found.
Example 2: A particle with unknown mass and charge moves with constant speed v = 1.9 x 106 m/s as it passes undeflected through a pair of parallel plates, as shown below. The plates are separated by a distance d = 6.0 x 103 m, and a constant potential difference V is maintained between them. A uniform magnetic field of magnitude B = 0.20 T directed into the page exists both between the plates and in a region to the right of them as shown. After the particle passes into the region to the right of the plates where only the magnetic field exists, its trajectory is circular with radius r = 0.10 m.
a. What is the sign of the charge of the particle? Check the appropriate space below.
___ Positive ___ Negative ___ Neutral ___ It cannot be determined from this information.
Justify your answer.
b. On the diagram above, clearly indicate the direction of the electric field between the plates.
c. Determine the magnitude of the potential difference V between the plates.
d. Determine the ratio of the charge to the mass (q/m) of the particle.
Force on a current carrying wire
· Since a charged particle moving perpendicular to a magnetic field experiences a force due to the field, a current carrying conductor perpendicular to a magnetic field will experience a force since a current is moving charge. The magnitude of the force depends upon the strength of the field, the current, and the length of the conductor in the field (F=BIl). The direction of the force can be found using the right hand rule. Point fingers in the direction of the magnetic field, thumb in the direction of the current (flow of positive charge), and your palm will point in the direction of the force.
· Example 3: A rail gun is a device that propels a projectile using a magnetic force. A simplified diagram of this device is shown below. The projectile in the picture is a bar of mass M and length D, which has a constant current I flowing through it in the +ydirection, as shown. The space between the thin frictionless rails contains a uniform magnetic field B, perpendicular to the plane of the page. The magnetic field and rails extend for a distance L. The magnetic field exerts a constant force F on the projectile, as shown.
a. In what direction must the magnetic field B point in order to create the force F? Explain your reasoning.
Use the following values in answering the next two questions.
B=5T L=l0m 1=200A M=0.5 kg D=l0cm
b. Calculate the magnitude of the acceleration of the bar while it is on the track.
c. Calculate the speed of the bar when it reaches the end of the rail.
Magnetic force between two parallel conductors
· Since a current carrying wire produces a magnetic field, two parallel wires each carrying a steady current exert forces on each other. Application of the right hand rules will show that the forces are attractive if the currents are in the same direction and repulsive if the currents are in opposite directions.
· Example 4: Two long parallel wires each carry a current of I. If both currents are doubled, how does the magnitude of the force on each wire change?
Galvanometer
· A galvanometer is a device used in the construction of both analog ammeters and voltmeters. In its simplest form, a galvanometer consists of a wire coil situated in a magnetic field. When current passes through the coil, torque due to the magnetic force on a current carrying wire causes the coil to twist. The angle to which the coil rotates depends upon the magnitude of the current.